Marine Corps General Joseph Dunford testifies during the Senate Armed Services committee nomination hearing to be chairman of the Joint Chiefs of Staff on Capitol Hill in Washington, July 9, 2015. Reuters/Yuri Gripas

U.S. Marine General Joseph Dunford played down the chances of Russia joining the U.S.-led air campaign against Islamic State in Iraq in the near future as he made his first trip to Iraq as top U.S. military official.

Russia's military intervention in Syria and its participation in a new Baghdad-based intelligence-sharing cell with Iran, Syria and Iraq has raised concerns in Washington that its Cold War rival is gaining influence in the Middle East.

Iraqi Prime Minister Haider al-Abadi said on Oct. 1, the same day Dunford took over as chairman of the Joint Chiefs of Staff, that he would welcome Russian air strikes against Islamic State militants in his country.

But Dunford said U.S. officials had since been reassured that Abadi had made no such request to Moscow.

"Subsequent to that, U.S. officials engaged Abadi and he did not request Russian air strikes," Dunford told reporters traveling with him.

Russia's military intervention in Syria has radically changed the landscape in the U.S.-led campaign against Islamic State, which seized vast tracts of Iraq and Syria last year.

Iraqi officials are frustrated with the pace and depth of the U.S. military campaign against Islamic State.

Iranian-backed Shi'ite militias leading the fight against Islamic State in Iraq say the United States lacks the decisiveness and the readiness to supply weapons needed to eliminate militancy in the region. Washington denies this.

A senior Iraqi parliamentary figure said last week that Baghdad had already begun bombing Islamic State jihadists with the help of a new intelligence centre in Baghdad staffed by Russian, Iraqi, Iranian and Syrian officials.

Dunford landed about half an hour later than planned in Erbil, capital of Iraqi Kurdistan, after his military aircraft was rerouted by air traffic controllers in Baghdad who were unfamiliar with his flight plans.

Dunford said he was looking forward to getting an update on the battle against Islamic State.

"Clearly, being in the job about two weeks, one of the things I wanted to do is go over here, get eyes on the ground," he said.

U.S. strategy in Iraq and in Syria hinges on supporting local ground forces, backed by U.S.-led coalition air strikes, to recapture ground from Islamic State, which has swept through northern Iraq and in May captured the city of Ramadi.

In recent days, U.S. officials have cited progress by Iraqi forces and militia recapturing parts of the Baiji oil refinery and they have noted incremental gains around the city of Ramadi.

But the overall campaign against Islamic State is moving slowly and major objectives, such as retaking the city of Mosul, appear distant.

Dunford was cautious in his comments to reporters before landing, saying he wanted to hear from U.S. and Iraqi officials on the ground. He cited recent operations in Baiji and Ramadi.

"I want to know how those are going, want to get a sense for where we are," he said.

Kurdish forces in Iraq have emerged as one of America's strongest partners in the fight against Islamic State and Dunford praised their bravery as he met the Kurdistan region's President Massoud Barzani.

"I hope coming here so soon after I assumed my new position indicates to you how important this endeavor is to us," Dunford told Barzani.

But even in Iraq's Kurdistan region, signs of political fracturing are mounting and an economic crisis has sent people onto the streets in protest.